Logic

Basic Logic

Inductive Reasoning

With inductive reasoning, our aim is to arrive at conclusions about our subject based on the observations of specific supporting instances. These conclusions are often based on generalizations concerning a set of data.

As an example, consider the inductive reasoning approach one might take in recognizing which of the three local television weather forecasters was most accurate in predicting the daily high temperatures. If you studied their forecasts every day for two weeks and then compared their predictions with the official high temperatures reported by the local weather service, you could begin to arrive at a conclusion on which forecaster was the most accurate. This is inductive reasoning in a nutshell, as the observer moves from specific observations—the comparison of the daily predictions with the actual daily temperatures—to generalizations. In this case, the final conclusion might be that one of the three forecasters was better at predicting the daily high temperature. Simple, right?

This example, however, brings other questions into the discussion.

  • Is two weeks of data enough to form a valid conclusion?
  • Were the forecasters predicting the weather for similar geographic areas?
  • Did the news agencies provide each of the forecasters with sufficiently sensitive equipment?

The reliability of an arguer’s conclusion depends on the quality and quantity of the observations, and those factors are what sometimes makes some inductive leaps logically faulty. If the sample size is too small, for instance, an arguer could be guilty of committing the common logical fallacy of “hasty generalization,” or drawing a conclusion from an incomplete or inadequate body of data.

It is important to note that induction is a reasoning process, and not necessarily a strategy for developing an essay. It is used to arrive at generalizations that suggest probabilities—not certainties. If, for instance, I go hunting for a new house in a planned subdivision here in Florida and I observe that most of the homes follow one of three basic floorplans, then it stands to reason that I will probably live in a home that follows one of those plans should I choose to buy there. That doesn’t mean, however, that there might not also be some homes which were built independently and which follow a different floorplan. Logic merely suggests that I would find myself in one of the more common models. (13)

To avoid making hasty generalizations, writers should be thorough in their research and careful in their organization and their positioning of supporting materials.

The two most common forms of basic logic that we apply in our daily lives and our written arguments are induction and deduction. Of these two forms of reasoning, we far more frequently use induction in supporting our views.(1)

Directions: Select each header to reveal information on each topic.

Deductive Reasoning

Deductive arguments seek a greater degree of certainty than their inductive counterparts. They often begin with a general statement that can be applied to a number of specific situations. Typically, deductive arguments take the form of the simple syllogism, which looks like this:

Major Premise: Truth about a large group.

Minor Premise: Truth about a specific member of that group.

Conclusion: Considered valid if the connections and conditions between the major and minor premises are true.

Here is an example of the simple syllogism:

Major Premise: Students scoring above a 3.0 GPA in their English classes at FSCJ need not take the CLAST exam to enter one of Florida’s public universities.

Minor Premise: Derek has a 3.5 GPA in his English classes at FSCJ.

Conclusion: Derek need not take the CLAST exam to enter a Florida public university.

Deductive arguments are only as strong as their premises, however, and while an argument may be logical, it can also be faulty. For instance, if the premises listed above are not true (Derek might have a 2.8 GPA, for instance), then the argument lacks validity. Or, perhaps Florida’s newest public university, Florida Polytechnic, has decided to independently create higher admissions standards than its state-wide counterparts. Once again, we can see that the quality of the observations is critical in determining the validity of the deductive argument.

Creating logical, reasonable arguments is often predicated on finding a sufficient body of specific, credible, and relevant supporting materials upon which to base your views. In the next pages of this learning module, we can further explore the components of basic logic and identify the many types of logical fallacies that we encounter on a daily basis. (13)

The Principles of Logic

So what are these principles of reasoning that are part of logic? There are many such principles, but the main (not the only) thing that we study in logic are principles governing the validity of arguments â€”whether certain conclusions follow from some given assumptions.

For example, consider the following three arguments:

If Tom is a philosopher, then Tom is poor. Tom is a philosopher. Therefore, Tom is poor.

If K>10, then K>2.
K>10.
Therefore, K>2.

If Tarragona is in Europe, then Tarragona is not in China. Tarragona is in Europe. Therefore, Tarragona is not in China.

These three arguments here are obviously good arguments in the sense that their conclusions follow from the assumptions. If the assumptions of the argument are true, then the conclusion of the argument must also be true. A logician will tell us that they are all cases of a particular form of argument known as “modus ponens” :

If P, then Q.

P.

Therefore, Q.

We shall discuss validity again later on. It should be pointed out that logic is not just concerned with the validity of arguments. Logic also studies consistency, and logical truths, and properties of logical systems such as completeness and soundness. But we shall see that these other concepts are also very much related to the concept of validity. (13)

Formal and Informal Logic

Sometimes a distinction is made between informal logic and formal logic . The term “informal logic” is often used to mean the same thing as critical thinking. Sometimes it is used to refer to the study of reasoning and fallacies in the context of everyday life. “Formal logic” is mainly concerned with formal systems of logic. These are specially constructed systems for carrying out proofs, where the languages and rules of reasoning are precisely and carefully defined. Sentential logic (also known as “Propositional logic”) and Predicate Logic are both examples of formal systems of logic.

There are many reasons for studying formal logic. One is that formal logic helps us identify patterns of good reasoning and patterns of bad reasoning, so we know which to follow and which to avoid. This is why studying basic formal logic can help improve critical thinking. Formal systems of logic are also used by linguists to study natural languages. Computer scientists also employ formal systems of logic in research relating to artificial intelligence. Finally, many philosophers also like to use formal logic when dealing with complicated philosophical problems, in order to make their reasoning more explicit and precise. (13)